
where \(\lbrace g_i\rbrace _{1\le i \le N}\)  are independent Gaussian random variables \(\mathcal {N}(0,2)\) , and \(\lbrace \chi _{k\beta }\rbrace _{1\le k\le N-1}\)  are independent \(\chi \) -distributed random variables with shape parameter \(k\beta \)  and independent of \(\lbrace g_i\rbrace _{1\le i \le N}\) . Then, Dumitriu and Edelman [1]} proved that eigenvalue probability distribution of \(H_{\beta }^{tri}\)  is (REF ) with \(\beta >0\) . For related topics of G\(\beta \) E, see [2]} and [3]}.
